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• Svex-select

Svex-select-replace-indices

Signature

(svex-select-replace-indices x indices) → new-x

Arguments

x — Guard (svex-select-p x).

indices — Guard (svexlist-p indices).

Returns

new-x — Type (svex-select-p new-x).

Definitions and Theorems

Function: svex-select-replace-indices

(defun svex-select-replace-indices (x indices)
 (declare (xargs :guard (and (svex-select-p x)
                             (svexlist-p indices))))
 (declare (xargs :guard (equal (len indices)
                               (len (svex-select->indices x)))))
 (let ((__function__ 'svex-select-replace-indices))
  (declare (ignorable __function__))
  (b* ((x (svex-select-fix x)))
   (svex-select-case
      x
      :var x
      :part
      (change-svex-select-part
           x
           :lsb (car indices)
           :subexp
           (svex-select-replace-indices x.subexp (cdr indices)))))))

Theorem: svex-select-p-of-svex-select-replace-indices

(defthm svex-select-p-of-svex-select-replace-indices
  (b* ((new-x (svex-select-replace-indices x indices)))
    (svex-select-p new-x))
  :rule-classes :rewrite)

Theorem: svex-select-replace-indices-of-svex-select->indices

(defthm svex-select-replace-indices-of-svex-select->indices
  (equal (svex-select-replace-indices x (svex-select->indices x))
         (svex-select-fix x)))

Theorem: svex-select->indices-of-replace-indices

(defthm svex-select->indices-of-replace-indices
 (implies
  (equal (len indices)
         (len (svex-select->indices x)))
  (equal
      (svex-select->indices (svex-select-replace-indices x indices))
      (svexlist-fix indices))))

Theorem: svex-select-replace-indices-of-svex-select-fix-x

(defthm svex-select-replace-indices-of-svex-select-fix-x
  (equal (svex-select-replace-indices (svex-select-fix x)
                                      indices)
         (svex-select-replace-indices x indices)))

Theorem: svex-select-replace-indices-svex-select-equiv-congruence-on-x

(defthm
      svex-select-replace-indices-svex-select-equiv-congruence-on-x
  (implies (svex-select-equiv x x-equiv)
           (equal (svex-select-replace-indices x indices)
                  (svex-select-replace-indices x-equiv indices)))
  :rule-classes :congruence)

Theorem: svex-select-replace-indices-of-svexlist-fix-indices

(defthm svex-select-replace-indices-of-svexlist-fix-indices
  (equal (svex-select-replace-indices x (svexlist-fix indices))
         (svex-select-replace-indices x indices)))

Theorem: svex-select-replace-indices-svexlist-equiv-congruence-on-indices

(defthm
   svex-select-replace-indices-svexlist-equiv-congruence-on-indices
  (implies (svexlist-equiv indices indices-equiv)
           (equal (svex-select-replace-indices x indices)
                  (svex-select-replace-indices x indices-equiv)))
  :rule-classes :congruence)